Study on the conditional autocorrelation and the cross-correlation of biphotons

Wei-Kai Huang^1*, Teng-Jen Shih¹, Yi-Min Lin¹, Kai-Bo Li¹, Chia-Yu Hsu¹, Jia-Mou Chen¹, Pei-Yu Tu¹, Thorsten Peters², Ite A. Yu^1,3

¹Department of Physics, National Tsing Hua University, Hsinchu, Taiwan
²Institut für Angewandte Physik, Technische Universität Darmstadt, Hochschulstraße 6, 64289 Darmstadt, Germany
³Center for Quantum Science and Technology, Hsinchu, Taiwan

* Presenter:Wei-Kai Huang, email:wkhuang97@gmail.com

Under the various cross-correlation functions (CCFs) of biphotons, we systematically studied how they can relate to the conditional auto-correlation functions (CACFs) of the heralded single photons. The CACF is an essential figure of merit to verify how pure the single photon source is. In our experiment, we utilize a hot atomic vapor to develop a biphoton source, which emits pairs of heralding and heralded single photons via the spontaneous four-wave mixing (SFWM) process. According to our intuition, the 2-fold coincidence should result in the 3-fold coincidence. Hence, we hypothesized that there would be a relationship between them, which enables us to use experimental data of the CCF to predict the CACF. The hypothesis prompts us to propose an analytical expression derived from general theory. With the analytical expression, we utilized the experimental data of CCF to predict CACF, and the predicted CACF well matches the measured counterpart. No matter what kind of process it is, i.e., SFWM or spontaneous parametric-down conversion, and what kind of material it is, i.e., atomic vapor, solid-state crystal, or integrated photonic device, the analytical expression is always valid. Instead of taking a long time to accumulate CACF’s data (typically more than two or three hours), we can now take a much shorter time (typically two or three minutes) to accumulate CCF’s data to obtain the CACF. Our result provides an effective method to predict the CACFs from the CCFs. This work has advanced the knowledge of quantum technology using biphotons or heralded single photons.

Keywords: autocorrelation, cross-correlaiton, biphoton, SFWM, heralded single photons